Actuarial Pricing of Non-Proportional Reinsurance Treaties Using R

This work provides a thorough overview of pricing non-proportional reinsurance treaties, focusing on both excess of loss per risk and cumulative catastrophe treaties, with a slight emphasis on the latter. Practical examples are given for each of the different methods, with step by step calculations, programming applications and the associated code using the language R. The paper summarizes the mathematical risk theory for each of the methods and explains thoroughly its relevance to the applied methods, thus striking the right balance between theory and applications. Topics covered include: experience rating (pure burning cost, indexed burning cost, triangulated burning cost), distribution methods (collective risk theory, modelling the number and severity of losses, stop-loss transform), exposure rating, exposure curves, MBBEFD, increased limits rating, extreme value theory, Pareto rating, the Peaks Over Thresholds method, Hill plots, choosing the appropriate threshold, return level plots, sensitivity of quantiles, the Panjer algorithm, detailed derivation and calculation of pure premiums of XL and Cat XL treaties, legal features, catastrophe models, payback method and loadings.